Finite Group DatabasebetaFinite Group DatabasebetaOrder 1664.
552 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 185 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11718639 | C2 | semidirect |
| 5. #11718606 | C2 | semidirect |
| 6. #11718606 | C2 | semidirect |
| 7. C22⋊C4×Dic13 | C2 | semidirect |
| 8. C22⋊C4×Dic13 | C2 | semidirect |
| 9. C4×#6101 | C2 | semidirect |
| 21. #88189 | C4 | semidirect |
| 44. C22×Dic13 | C2×C4 | semidirect |
| 56. C22⋊Dic13 | C2×C4 | semidirect |
| 58. #6101 | C2×C4 | semidirect |
| 188. C13 | #2374 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88189 | 2 |
| C13×#390 | 2 |
| #11718881 | 2 |
| #11718639 | 2 |
| #11718606 | 2 |
| C22⋊C4×Dic13 | 2 |
| C4×#6101 | 2 |
| #2374 | 13 |